Prediction of vicinal proton–proton coupling constants 3 J HH from density functional theory calculations

Vicinal coupling constants ³ J _HH have been calculated at the optimized geometries for a series of selected molecules with the aim of developing a practical procedure for predicting this kind of coupling. Calculations of couplings and optimizations of molecular geometries have been carried out at the DFT/B3LYP level using a moderate sized basis set. When the Fermi contact contributions to ³ J _HH calculated for 25 mono- and 23 1,1-di-substituted ethanes are multiplied by a factor of 0.904, the corresponding predicted couplings J ^pre are in good agreement with the experimental J ^exp couplings, with standard deviation σ of 0.10?Hz. When such a comparison is carried out for the remaining sets of molecules the σ deviation increases to 0.26?Hz for a dataset of 21 couplings from 11 monosubstituted cyclohexanes, to 0.19?Hz for a dataset of 40 couplings from 6 norbornane type molecules and to 0.25?Hz for a dataset of 54 couplings from 14 three-membered rings. For the complete dataset of 163 couplings the?σ?deviation amounts to 0.20?Hz. This figure is further reduced to 0.17?Hz by adding to the J ^pre coupling a small correction given by the term ?0.15cos?, depending on the dihedral angle ? between the coupled protons. A larger σ deviation of 0.31?Hz was reported for the best empirically parameterized extended Karplus equation. DFT J ^pre values could be further improved by more accurate calculations for the pertinent substituted ethane constituents of the molecule in question by applying a substituent effect model.     

Intramolecular surfaces for vicinal proton–proton coupling constants 3JHH

Equations for the intramolecular surfaces of the ³J_HH coupling constants in ethane, ethylene, and acetylene are formulated, and the corresponding coefficients are estimated from calculations at the DFT/B3LYP level. The chosen variables are changes in bond lengths, in the torsion angle φ between the coupled protons H_a and H_b, in bond angles, and in dihedral angles. The ³J_HH surface of ethane is formulated as an extended Karplus equation with the coefficients of a truncated Fourier series on the torsion angle φ expanded as second-order Taylor series in the chosen variables taking into account the invariance of ³J_HH under reflections and rotations of nuclear coordinates. Partial vibrational contributions from linear and square terms corresponding to changes in the geometry of the H_a ? C_a ? C_b ? H_b fragment are important while those from cross terms are small with a few exceptions. The ³J_HH surface of ethane is useful to predict contributions to ³J_HH from changes in local geometry of derivatives but vibrational contributions are predicted less satisfactorily. The predicted values at the B3LYP/BS2 level of the ³J_HH couplings (vibrational contributions at 300 K) from equilibrium geometries are 9.79 (?0.17) for acetylene, and 17.08 (1.93) and 10.73(0.93) for the trans and cis couplings of ethylene.     

Spin–spin coupling constants in linear substituted HCN clusters

The indirect nuclear spin–spin coupling constants of homogeneous hydrogen-bonded HCN clusters are compared with those of inhomogeneous HCN clusters where one of the terminal HCN molecules is substituted by its isomer HNC and by LiCN. Both the intra- and intermolecular (across the hydrogen bond) coupling constants are calculated for the linear form of the clusters containing up to three molecular monomers using different hybrid DFT functionals. The geometry of the monomers and clusters is optimised at the B3LYP/6-311++G(d,p) level. The effect of substitution by the ionic compound LiCN on the coupling constants of HCN is found to be more pronounced than that by HNC. The Ramsey parameters that form the total spin–spin coupling constants are also analysed individually. Among the four Ramsey parameters, the Fermi Contact term is found to be the dominant contributor to the total coupling constants in most cases. The presence of LiCN in the cluster tends to decrease the intramolecular Fermi Contact values, while HNC increases the same in all dimers and trimers. The contributions of localised molecular orbitals have been analysed for the HCN–HNC cluster to obtain some additional insight about the SSCC transmission mechanism along the coupling pathway.     

NMR spin–spin coupling constants in microhydrated ortho-aminobenzoic acid

The influence of the hydrogen-bond formation on the NMR spin–spin coupling constants, including the Fermi contact, the diamagnetic spin–orbit, the paramagnetic spin–orbit and the spin dipole term, has been investigated for the ortho-aminobenzoic acid microhydrated with up to three water molecules. The one-bond and two-bond spin–spin coupling constants for several intra-molecular and across-the-hydrogen-bond atomic pairs are calculated employing high-level density functional theory in combination with the B3LYP functional with two different types of extended basis sets for each level of microhydration. The spin–spin coupling constants, in general, vary inversely with the hydrogen bond length. The Fermi contact term is found to be the dominant contributor to the total value of spin–spin coupling constant followed by the paramagnetic spin–orbit term. The variations of Fermi contact term and atomic charge distribution with size of microhydration follow quite similar trend. The effect of explicit solvation provided by microhydration has also been compared briefly with that of bulk implicit solvation obtained through polarised continuum model and mixed microhydration/continuum approach.     

Properties of the coupling constants of J/ψ→VP decays

Based on the branching fractions of J/ψ→VP from different experiments, we investigate the properties of the coupling constants of J/ψ→VP decays using a model-dependent approach. We find that the octet coupling constant, g8, of strong interaction is about twice larger than that of the singlet coupling constant g₁; the electromag- netic breaking parameters g_Eⁱ are larger than the mass breaking parameters g_Mⁱ, moreover, the three parameters of the electromagnetic effect are about equal, but the three parameters of the mass effect are obviously different and their uncertainties are also large; and the phase angle between strong and electromagnetic interactions is in the range of 70°-80°. It deepens our understanding of the coupling constant of J/ψ→VP decays.     

Assessment of DFT functionals with fluorine–fluorine coupling constants†

Density functional theory (DFT) calculations of nuclear magnetic resonance (NMR) spin–spin coupling constants (SSCCs) provide an important contribution for understanding experimentally observed values. It is known that calculated SSCCs using DFT methods correlate well with those experimentally measured. Unlike most of SSCCs, in fluorine compounds, fluorine–fluorine SSCC J_FF shows that the Fermi contact (FC) term is not dominant, particularly for J_FF in polyfluorinated organic molecules. In order to devise a DFT approach that would correctly reproduce the variation of SSCCs within a series of fluorine compounds, we test several DFT-based approaches, using different exchange and correlation functionals. Isotropic contributions to NMR fluorine–fluorine coupling constants (FC, spin-dipolar, SD, paramagnetic spin-orbit, PSO, and diamagnetic spin-orbit, DSO) have been calculated. Results show that DFT methods give appropriate values for ⁿJ_FF (n = 4 to 7), while for geminal and vicinal J_FF present large deviations from experimental values. For the latter SSCCs (²J_FF and ³J_FF), the four contributions (FC, SD, PSO and DSO) are analysed as a function of the local and nonlocal exchange in 1,1- and 1,2-difluoroethylene. Although FC term is not dominant for these SSCCs, the variation of this contribution with exchange is remarkable. On the other hand, SD and PSO contributions can be suitably computed without and with exact exchange, respectively.     

Antisymmetry and channel coupling contributions to the absorption for p+αd+3He

To understand recently established empirical p+α potentials, RGM calculations followed by inversion are made to study contributions of the d+³He reaction channels and deuteron distortion effects to the p+α potential. An equivalent study of the d+³He potential is also presented. The contributions of exchange non-locality to the absorption are simulated by including an phenomenological imaginary potential in the RGM. These effects alone strongly influence the shape of the imaginary potentials for both p+α and d+³He. The potentials local-equivalent to the fully antisymmetrised-coupled channels calculations have a significant parity-dependence in both real and imaginary components, which for p+α is qualitatively similar to that found empirically. The effects on the potentials of the further inclusion of deuteron distortion are also presented. The inclusion of a spin-orbit term in the RGM, adds additional terms to the phase-equivalent potential, most notably the comparatively large imaginary spin-orbit term found empirically.     

Two-, three-, and four-bond N–F spin–spin coupling constants in fluoroazines

Ab initio EOM-CCSD calculations have been performed to investigate 2-, 3- and 4-bond ¹⁵N–¹⁹F coupling constants in mono-, di-, and trifluoroazines. ²J(N–F) values are negative and are dominated by the Fermi-contact (FC) term. Absolute values of ²J(N–F) tend to decrease as the number of N atoms in the ring increases, and may also be influenced by the number and positions of C–F bonds. ³J(N–F) values are positive with three exceptions, are usually dominated by the FC term, and also tend to decrease as the number of N atoms increases. The three molecules which have negative values of ³J(N–F) have dominant negative paramagnetic-spin orbit (PSO) terms, and are structurally similar insofar as they have an intervening C–F bond between the N and the coupled F. ⁴J(N–F) values are negative because the PSO, FC, and spin-dipole (SD) terms are negative, with only one exception. Four molecules have significantly greater values of ⁴J(N–F). These are structurally similar with the coupled N bonded to two other N atoms. The computed EOM-CCSD ⁿJ(N–F) coupling constants are in good agreement with the few experimental values that are available.     

Molecular properties in the Tamm–Dancoff approximation: indirect nuclear spin–spin coupling constants

The Tamm–Dancoff approximation (TDA) can be applied to the computation of excitation energies using time-dependent Hartree–Fock (TD-HF) and time-dependent density-functional theory (TD-DFT). In addition to simplifying the resulting response equations, the TDA has been shown to significantly improve the calculation of triplet excitation energies in these theories, largely overcoming issues associated with triplet instabilities of the underlying reference wave functions. Here, we examine the application of the TDA to the calculation of another response property involving triplet perturbations, namely the indirect nuclear spin–spin coupling constant. Particular attention is paid to the accuracy of the triplet spin–dipole and Fermi-contact components. The application of the TDA in HF calculations leads to vastly improved results. For DFT calculations, the TDA delivers improved stability with respect to geometrical variations but does not deliver higher accuracy close to equilibrium geometries. These observations are rationalised in terms of the ground- and excited-state potential energy surfaces and, in particular, the severity of the triplet instabilities associated with each method. A notable feature of the DFT results within the TDA is their similarity across a wide range of different functionals. The uniformity of the TDA results suggests that some conventional evaluations may exploit error cancellations between approximations in the functional forms and those arising from triplet instabilities. The importance of an accurate treatment of correlation for evaluating spin–spin coupling constants is highlighted by this comparison.     

Analytic and “frozen” coupling constants in QCD up to NNLO from DIS data

Deep inelastic scattering data on the F ₂ structure function provided by the BCDMS, SLAC, and NMC Collaborations are analyzed in the nonsinglet approximation with the analytic and “frozen” modifications of the strong-coupling constant featuring no unphysical singularity (the Landau pole). Improvement of agreement between theory and experiment, with respect to the case of the standard perturbative definition of α _s considered recently, is observed and the higher-twist terms are shown to reduce at the next-to-next-to-leading order accuracy thus confirming earlier studies.     

Relation between the charged and neutral pion–nucleon coupling constants in the Yukawa model

In the Yukawa-model framework for NN forces, a simple relation between the charged and neutral pion–nucleon coupling constants is derived. The relation implies that the charged pion–nucleon constant is larger than the neutral one since the np interaction is stronger than the pp interaction. The derived value of the charged pion–nucleon constant shows a very good agreement with one of the recent measurements. In relative units, the splitting between the charged and neutral pion–nucleon constants is predicted to be practically the same as that between the charged and neutral pion masses. The charge dependence of the NN scattering length arising from the mass difference between the charged and neutral pions is also analyzed.     

Nuclear effects on J/ψ production in proton–nucleus collisions

The study of nuclear effects for J/ψ production in proton–nucleus collisions is crucial for a correct interpretation of the J/ψ suppression patterns experimentally observed in heavy-ion collisions. By means of three representative sets of nuclear parton distribution, the energy loss effect in the initial state and the nuclear absorption effect in the final state are taken into account in the uniform framework of the Glauber model. A leading order phenomenological analysis is performed on J/ψ production cross-section ratios R _W/Be (x _F) for the E866 experimental data. The J/ψ suppression is investigated quantitatively due to the different nuclear effects. It is shown that the energy loss effect with resulting in the suppression on R _W/Be (x _F) is more important than the nuclear effects on parton distributions in high x _F region. The E866 data in the small x _F keep out the nuclear gluon distribution with a large anti-shadowing effect. However, the new HERA-B measurement is not in support of the anti-shadowing effect in the nuclear gluon distribution. It is found that the J/ψ–nucleon inelastic cross section $\sigma^{J/\psi}_{\mathrm{abs}}$ depends on the kinematical variable x _F, and increases as x _F in the region x _F>0.2.     

The coupling of Chern–Simons theory to topological gravity

We couple Chern–Simons gauge theory to 3-dimensional topological gravity with the aim of investigating its quantum topological invariance. We derive the relevant BRST rules and Batalin–Vilkovisky action. Standard BRST transformations of the gauge field are modified by terms involving both its anti-field and the super-ghost of topological gravity. Beyond the obvious couplings to the metric and the gravitino, the BV action includes hitherto neglected couplings to the super-ghost. We use this result to determine the topological anomalies of certain higher ghost deformations of SU(N)$\mathit{SU}(N)$ Chern–Simons theory, introduced years ago by Witten. In the context of topological strings these anomalies, which generalize the familiar framing anomaly, are expected to be cancelled by couplings of the closed string sector. We show that such couplings are obtained by dressing the closed string field with topological gravity observables.     

Effects of vibrational averaging on coupled cluster calculations of spin–spin coupling constants for hydrocarbons

We present vibrationally corrected nuclear spin–spin coupling constants for four hydrocarbons with different types of carbon–carbon bonds calculated with coupled cluster (CC) theory. First, we perform a systematic basis set investigation on acetylene for all of the four contributions (Fermi-contact, spin-dipole, para- and diamagnetic spin–orbit) to the spin–spin coupling constants and subsequently choose basis sets of sufficient flexibility to describe converged electronic properties. Then, in order to describe the effects of vibrational motion for the studied molecules we perform a Taylor expansion in the normal coordinates up to second order – a method that is well known for both its quality and efficiency – and rigorously estimate the resulting contribution for all types of spin–spin coupling constants. Combined, this allows us to obtain highly accurate benchmark estimates of the spin–spin coupling constants for acetylene, ethylene, ethane, and cyclopropane. This work provides one of the first systematic benchmarks of zero-point vibrational contributions to spin–spin coupling constants in poly-atomic molecules using the reliable CC theory and it is thus an important reference for further research within in-silico spin–spin coupling constant determination. We note that earlier computational estimates of zero-point vibrational effects agree well with those presented here (for acetylene, ethylene, and cyclopropane) while vibrational corrections for ethane are reported for the first time.     

Determination of 3J(H3í, Pi+1) and 3J(H5í/5i, Pi) coupling constants in 13C-labeled nucleic acids using constant-time HMQC.

A novel 1H-13C correlated two-dimensional experiment, CT-HMQC-J, for the measurement of three-bond proton-phosphorus coupling constants in 13C-labeled DNA is described. The experiment is based on the intensity difference of 1H-13C cross peaks in the presence and absence of the proton-phosphorus coupling interaction during the constant-time period in HMQC experiment. The 3J(H, P) coupling constants can be easily extracted from the intensity ratios of the two experiments. The method has been applied to a uniformly 13C, 15N-labeled d(GGAGGAT) 7-mer DNA sample. The proton-phosphorus coupling constants determined from CT-HMQC-J, together with the other three-bond coupling constants, are used to determine beta and epsilon torsion angles. The introduction of beta and epsilon restraints has improved the convergence as well as the quality of d(GGAGGAT) structure.     

Vibrational spectra of an LiNO3–(CH3)2SO2 system

Raman and IR absorption spectra were studied and molecular relaxation characteristics of vibrations of the anion and solvent were calculated for an xLiNO₃–(1 – x)(CH₃)₂SO₂ system (x = 0.1, 0.2, 0.3, 0.4 M). It was found that it is impossible to increase the concentration of free ions involved in charge transfer in such a system by either increasing the temperature or changing the concentration composition in the studied range of x.     

Scale choice and collinear contributions to Mueller–Navelet jets at LHC energies

We investigate the stability under variation of the renormalization, factorization and energy scales entering the calculation of the cross section, at next-to-leading order in the BFKL formalism, for the production of Mueller–Navelet jets at the Large Hadron Collider, following the experimental cuts on the tagged jets. To find optimal values for the scales involved in this observable it is possible to look for regions of minimal sensitivity to their variation. We show that the scales found with this logic are more natural, in the sense of being more similar to the squared transverse momenta of the tagged jets, when the BFKL kernel is improved with a resummation of collinear contributions than when the treatment is at a purely next-to-leading order. We also discuss the good perturbative convergence of the ratios of azimuthal angle correlations, which are quite insensitive to collinear resummations and well described by the original BFKL framework.